Satellite positioning systems such as the global positioning system (GPS) use satellites in space to locate objects on earth. With GPS, signals from the satellites arrive at a GPS receiver and are used to determine the position of the GPS receiver. Currently, two types of GPS measurements corresponding to each correlator channel with a locked GPS satellite signal are available for civilian GPS receivers. The two types of GPS measurements are pseudorange, and integrated carrier phase for two carrier signals, L1 and L2, with frequencies of 1.5754 GHz and 1.2276 GHz, or wavelengths of 0.1903 m and 0.2442 m, respectively. The pseudorange measurement (or code measurement) is a basic GPS observable that all types of GPS receivers can make. It utilizes the C/A or P codes modulated onto the carrier signals. The measurement records the apparent time taken for the relevant code to travel from the satellite to the receiver, i.e., the time the signal arrives at the receiver according to the receiver clock minus the time the signal left the satellite according to the satellite clock.
The carrier phase measurement is obtained by integrating a reconstructed carrier of the signal as it arrives at the receiver. Thus, the carrier phase measurement is also a measure of a transit time difference as determined by the time the signal left the satellite according to the satellite clock and the time it arrives at the receiver according to the receiver clock. However, because an initial number of whole cycles in transit between the satellite and the receiver when the receiver starts tracking the carrier phase of the signal is usually not known, the transit time difference may be in error by multiple carrier cycles, i.e., there is a whole-cycle ambiguity in the carrier phase measurement. Various techniques have been developed to resolve this whole-cycle ambiguity. An excellent overview of such techniques is found in Chapter 7, Section 7.8, “Ambiguity Fixing,” in GPS Satellite Surveying, 3rd edition, by Alfred Leick, published by John Wiley & Sons, New York, 2004.
Thus, to navigate an object, a GPS receiver attached to the object receives GPS measurements from a multitude of satellites and these GPS measurements are processed by a computer system coupled to the GPS receiver to produce updates to the position of the object. To compute the updates to the position of the object, the range or distance between the GPS receiver and each of the multitude of satellites is calculated by multiplying a signal's travel time by the speed of light. These ranges are usually referred to as pseudoranges (false ranges) because the receiver clock generally has a significant time error which causes a common bias in the measured range. This common bias from the receiver clock error can be solved for along with the position coordinates of the GPS receiver as part of the normal navigation computation. Various other factors can also lead to errors or noise in the calculated range, including ephemeris error, satellite clock timing error, atmospheric effects, receiver noise and multipath error. With standalone GPS navigation, where the GPS receiver obtains code and/or carrier-phase ranges with respect to a plurality of satellites in view, without consulting with any reference station, one is usually very limited in ways to reduce the errors or noises in the ranges.
To eliminate or reduce these errors, differential operations are typically used in GPS applications. Differential GPS (DGPS) operations involve a base or reference station having a base or reference GPS receiver, a navigation system having a rover or navigation GPS receiver attached to the object being navigated, and a communication link between the reference station and the navigation system. The reference station is usually at a known position and the measurements obtained and/or corrections computed thereat are transmitted to and used by the navigation system to cancel out most of the error factors. Differential operations using carrier-phase measurements are often referred to as real-time kinematic (RTK) positioning/navigation operations.
The fundamental concept of Differential GPS (DGPS) is to take advantage of the spatial and temporal correlations of the errors inherent in the GPS measurements to cancel the noise factors in the pseudorange and/or carrier phase measurements resulting from these error factors. However, while the GPS satellite clock timing error, which appears as a bias on the pseudorange or carrier phase measurement, is perfectly correlated between the reference receiver and the user receiver, most of the other error factors are either not correlated or the correlation diminishes in wide-area applications, i.e., when the distance between the reference and user receivers becomes large.
To overcome the inaccuracy of the DGPS system in wide-area applications, various regional, wide-area, or global DGPS (hereafter referred to as wide-area DGPS or WADGPS) techniques have been developed. The WADGPS includes a network of multiple reference stations in communication with a computational center or hub. Error corrections are computed at the hub based upon the known locations of the reference stations and the measurements taken by them. The computed error corrections are then transmitted to users via communication link such as satellite, phone, or radio. By using multiple reference stations, WADGPS provides more accurate estimates of the error corrections.
With the errors more or less corrected using any of the stand-alone, the RTK, and/or the WADGPS system, the computer system coupled to the navigation GPS receiver typically computes an update to the receiver position once in each of a series of epochs. A number of different techniques have been developed to update the position of the GPS receiver using the GPS carrier-phase measurements. Examples of these techniques are the least-squares and Kalman filter processes. The least-squares technique is addressed at length in Chapter 4, “Least Squares Adjustments,” in GPS Satellite Surveying, 3rd edition, by Alfred Leick, published by John Wiley & Sons, New York, 2004. The Kalman Filter is addressed briefly at the end of the chapter. In a conventional GPS navigation system, the position of the GPS receiver is typically updated at the rate of 1 Hertz, i.e., one update per second. For objects with moderate and high dynamics, it is often desired that the position updates are calculated at a higher rate. Because of the complexity of a full least-squares or Kalman filter process, however, the computational capabilities of the computer system can be exceeded if the position updates are computed at a rate significantly higher than the 1 Hertz rate. Therefore, there is a need for a satellite navigation technique that significantly increases the rate at which accurate position updates are produced while minimizing computational complexities.